CF 403D Beautiful Pairs of Numbers

CF 403D Beautiful Pairs of Numbers"/>

CF 403D Beautiful Pairs of Numbers

The sequence of integer pairs (a₁, b₁), (a₂, b₂), ..., (a_k, b_k) is beautiful, if the following statements are fulfilled: 

• 1 ≤ a₁ ≤ b₁ < a₂ ≤ b₂ < ... < a_k ≤ b_k ≤ n, where n is a given positive integer; 
• all numbers b₁ - a₁, b₂ - a₂, ..., b_k - a_k are distinct. 

For the given number n find the number of beautiful sequences of length k. As the answer can be rather large, print the remainder after dividing it by 1000000007 (10⁹ + 7).

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